This thesis focuses on combinatorial enumeration of lattice paths using the Constant Term method. In particular we make use of the Bethe Ansatz, an Ansatz given by a linear combination of solutions to the free ``no ...

Multitype branching processes describe the evolution of populations in which individuals give birth independently according to a probability distribution that depends on their type. In this thesis, we consider the extinction ...

The focus of this thesis is the study of Markov modulated fluid models in the performance modelling of ad hoc telecommunications networks – that is networks where nodes communicate via multi-hop routes as there is no central ...

The traditional activity of model selection aims at discovering a single model superior to other candidate models. In the presence of noise in data, however, it is typically difficult to declare a single model significantly ...

The smooth 4-dimensional Poincare conjecture states that if a smooth 4-manifold is homeomorphic to the 4-sphere then it is diffeomorphic to the standard 4-sphere. Historically, one of the most promising families of potential ...

A mathematical model which captures how the immune response controls influenza infection is essential for predicting the effects of pharmaceutical interventions, and alleviating the public health burden of the disease. ...

Public transit skip-stop operations were first introduced to cope with the traffic congestion. Skip-stop operations take place when each vehicle services a subset of stations along a route, which together covers all stations. ...

Ideally, a parametric model for a biological system enables prediction of system behaviour for conditions where we lack observations. This necessitates first estimating parameters from some limited data series subject to ...

In this thesis we primarily focus on developing tractable dynamic market models, together with applications of these models. We also address several open questions concerning the statistical properties of static market ...

Magnetic monopoles are solutions to first order non-linear partial differential equations called the Bogolmonyi equations. Magnetic monopoles in three dimensional hyperbolic space can be treated as instantons invariant ...